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Mathematics - Circle Question with Solution | TestHub

MathematicsCircleTangent & NormalMedium2 minQB

MathematicsMediumsingle choice

In triangle $A BC$ with $A B = A C = 5, BC = 6$ , let the locus of an interior point whose distance from $BC$ is the geometric mean of its distances from $A B, A C$ be extended to its defining circle. If the tangents to that circle at $B$ and $C$ meet at $T$ , find $[TBC]$ .

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Answer:

Solution:

With $A = (0, 4), B = (- 3, 0), C = (3, 0)$ the circle is $2 x^{2} + 2 y^{2} + 9 y - 18 = 0$ . Its tangents at $B, C$ are $- 4 x + 3 y - 12 = 0$ and $4 x + 3 y - 12 = 0$ . They meet at $T = A$ . Hence $[TBC] = \frac{1}{2} (6) (4) = 12$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: QB

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